A car has a mass of 850 kg and its engine can generate a maximum power of 35kW. The total resistance to motion of the car is modelled as kvN where vms-1 is the speed of the car and k is a constant. When the car is moving in a straight line on a straight horizontal road, the greatest constant speed that it can
attain is 25 ms-

(1) Show that k= 56.

(ii) Find the greatest possible acceleration of the car on the road at an instant when it is moving with a speed of 15 ms -1

A trailer of mass 240 kg is attached to the car by means of a light inextensible tow bar which is parallel to the surface of the road. The resistance to motion of the trailer is modelled as a constant force of magnitude
350N.

The car and trailer move on the horizontal road. At a certain instant the car's engine is working at a rate of 30kW and the acceleration of the car is 0.2 ms=2

(iii) (a) Find the speed of the car at this instant.

(b) Find the magnitude of the tension in the tow bar at this instant.

The car and trailer now move in a straight line on a straight road inclined at 8° to the horizontal.

(iv) Find the difference between their greatest possible constant speed travelling up the slope and their greatest possible constant speed travelling down the slope,